Management is inward facing, paying attention to the people you are responsible for, and knowing the right thing that's needed at the right time.
"If you want to build a ship, don't drum up people to collect wood and don't assign them tasks and work, but rather teach them to long for the endless immensity of the sea." - Antoine de Saint-Exupery
Leadership is building the boat, management is making sure the boat gets built, on time, on budget, with the proper permits and inspections, training and safety gear, along with bi-weekly status reports to customers.
Some people confuse one with the other, but to me they're distinct and this is a rough sketch of how I see them as different.